Magnetoroton is a gapped neutral excitation in the fractional quantum Hall effect (FQHE) and plays an important role in the low-energy physics of the latter. It was first predicted theoretically by Girvin, MacDonald, and Platzman and later observed in experiments. Originally proposed as a charge density wave, it has recently been shown to carry spin two and can be considered a massive graviton excitation.  

We investigated the magnetoroton in the 𝜈=2/7, 𝜈=2/9 Jain’s states. In contrast to the common lore, originally formulated by Girvin, MacDonald, and Platzman as the “single-mode approximation,” we find that the spectra of these Jain’s states contain not one but two magnetorotons. In particular, there is a high-energy magnetoroton, which we found to exist also in the 𝜈=1/4 Fermi-liquid state. We also numerically confirm the exact gravitational sum rules of FQHE.

We reconsider the composite fermion theory of general Jain sequences with filling factor 𝜈=𝑁/(4⁢𝑁±1). We show that Goldman and Fradkin's proposal of a Dirac composite fermion leads to a violation of the Haldane bound on the coefficient of the static structure factor. To resolve this apparent contradiction, we add to the effective theory a gapped chiral mode (or modes) that already exists in the Fermi liquid state at 𝜈=1/4. We interpret the additional mode as an internal degree of freedom of the composite fermion, related to area-preserving deformations of the elementary droplet built up from electrons and correlation holes. In addition to providing a suitable static structure factor, our model also gives the expected Wen-Zee shift and a Hall conductivity that manifests Galilean invariance. We show that the charge density in the model satisfies the long-wavelength version of the Girvin-MacDonald-Platzman algebra.

Raman scattering provides an important probe of the fractional quantum Hall effect. In addition to the enegy spectrum of magnetoroton exciitations, polarized Raman scattering can also measure the spin of the magnetoroton. The problem of Raman scattering involves physics at two vastly different scales: the scale of the energy of the photons and the energy scale of the FQHE. In a certain regime, one can ''factor out'' the calculable physics at the photon energy scale, reducing the problem to the calculation of the spectral density of a pair of spin-2 operators on a single Landau level. Thus Raman scattering does not measure the density response but a certain ''stress response.'' This is reminiscent of Haldane's proposal that the long-wavelength magnetoroton is a kind of ''emergent graviton.'' We will argue that the single mode approximation does not work for Jain states near ν=1/4. In the simplest scenario these states contain two magnetoroton modes, which have different chirality for ν=n/(4n-1) and the same chirality for ν=n/(4n+1), measureable in polarized Raman scattering. Polarized Raman scattering, in principle, can also help the determination of the nature of the ν=5/2 plateau.

The fractional quantum Hall (FQH) states in a two-dimensional electron gas under a strong magnetic field are topologically ordered gapped states. These states are understood using the concept of composite fermions, introduced by Jain, and further explored by Halperin, Lee, and Read (HLR) for the half-filling state, predicting the Fermi-liquid behavior of quasi-particles. However, the composite fermion theory has issues, particularly with particle-hole symmetry in the lowest Landau level (LLL). The Dirac composite fermion model, proposed by Son, addresses this problem. We investigated the Dirac composite fermion model to calculate physical quantities for incompressible states in Jain's sequences at large N, explicitly satisfying particle-hole symmetry, reproducing universal topological coefficients, and confirming the magnetoroton dispersion relation with experimental results. We also predict the higher spin model of FQHs using the Dirac composite fermion model.

We show how a diffeomorphism invariance of the quantum Hall systems, together with topological consideration, put strong constraints on the physics that goes beyond the Chern-Simons action. We show how the Hall conductivity at finite wavenumbers is constrained. We also derive new sum rules that govern the spectrum of low-energy excitations in a fractional quantum Hall system. We show how these sum rules can be saturated by a single quasiparticle which can be interpreted as a massive emergent graviton. We identify this massive graviton with the magneto-roton and discuss consequences for experiments.

This groundbreaking research confirms the existence of novel topological-protected interface states between two Weyl semimetals in a photonic lattice different from the well-known Fermi arcs. We investigate a trilayer photonic grating whose relative displacements between adjacent layers play the role of two synthetic momenta; the 1D system emulates 3D topological crystals, including Weyl semimetals, nodal line semimetals, and Chern insulators. The research paves the way for a better understanding of topological phenomena in photonic lattices and related systems, promising potential applications in designing novel photonic devices and materials with topological features.

This study delves into the physics of photonic band structures in moiré patterns formed by overlapping two one-dimensional photonic crystal slabs with differing periods. The band structure is determined by the interplay of coupling mechanisms within and between layers, modifiable by the spacing between them. Through an effective Hamiltonian, the system's key physics is captured accurately, matching numerical simulations. Particularly noteworthy are "magic distances" where photonic flatbands emerge across the Brillouin zone of the moiré superlattice. These flatband modes are highly localized within a moiré period. Additionally, a single-band tight-binding model is proposed to describe moiré minibands, with tunable tunneling rates via interlayer strength. The findings suggest that bilayer photonic moiré band structures can be engineered akin to electronic/excitonic systems, opening avenues for exploring many-body physics at photonic moiré flatbands and developing optoelectronic devices.

The Tkachenko wave is a special phonon of the superfluid vortex lattice with a quadratic dispersion; it is a shared Nambu-Goldstone boson of magnetic translation and boson conservation symmetries. A nonlinear theory of the Tkachenko mode based on noncommutative field theory with the dipole symmetry is formulated, and it is shown that the excitation is stable.

Employing the fracton-elastic duality, we develop a low-energy effective theory of a zero-temperature vortex crystal in a two-dimensional bosonic superfluid which naturally incorporates crystalline topological defects. We extract static interactions between these defects and investigate several continuous quantum transitions triggered by the Higgs condensation of vortex vacancies/interstitials and dislocations. We propose that the quantum melting of the vortex crystal towards the hexatic or smectic phase may occur via a pair of continuous transitions separated by an intermediate vortex supersolid phase.

The quantum Hall effect in curved space is theoretically interesting but hard to observe. Strained graphene, which mimics Dirac fermions in curved space under a pseudo-gauge field, offers a potential solution. This work analytically derives a low-energy Hamiltonian from the tight-binding model, matching it with curved-space predictions. Numerical calculations show the Landau level spectrum agrees well with these predictions.

Additionally, half-integer quantized flux vortices in honeycomb lattices, induced by altering coupling signs, can trap localized states using inhomogeneous strain. This enhances the localization of non-Abelian anyons in Kitaev's model.

These results provide a testbed for fundamental physics, accurately replicating excitations' energies and degeneracies when considering the effective hyperbolic geometry induced by strain. An external magnetic field further maps this inhomogeneous metric.

 We presented a formalism for calculating the transport properties of bilayer graphene (BLG). Starting from the Kadanoff-Baym equations, we derived the quantum Boltzmann equation and obtained the full collision operators. We have formulated the Boltzmann equation for the electrical and thermal conductivity and the shear viscosity of BLG. We calculated the collision integrals numerically to derive the quantum transport coefficients. We also proposed a simple two fluids model that captures the essential physics of bilayer graphene. Recent experiments on quantum transports of BLG confirmed our results. We also applied formalism to multi-layer graphene systems.